Name : Jeseeka Shah, Sanjana Chaudhari and Supreeth Murugesh
Instructor : Prof. Amin Karimpour
Class : Probability Theory and Introductory Statistics
School : Northeastern University - College of Professional Studies
Date of submission : 12 December, 2021
Dataset
# Loading the dataset
superstore_2011_2015 <- read.csv("Dataset/superstore-2011-2015.csv")
# Considering only the US market for Analysis
superstore_2011_2015 <- filter(superstore_2011_2015, superstore_2011_2015$Market == "US")
# Omitting NA values
superstore_2011_2015 <- na.omit(superstore_2011_2015)
# Calculating Total Sales
superstore_2011_2015 <- mutate(superstore_2011_2015,
Total_Sales = superstore_2011_2015$Sales * superstore_2011_2015$Quantity)Descriptive Statistics of numerical variables
columnNames <- c('Sales', 'Discount', 'Profit', 'Shipping Cost', 'Total Sales')
rowNames <- c('Mean', 'Standard Deviation', 'Range', 'Median')
# Descriptive statistics of Discount
meanDiscount <- round(mean(superstore_2011_2015$Discount),2)
stdDiscount <- round(sd(superstore_2011_2015$Discount),4)
rangeDiscount <- round(max(superstore_2011_2015$Discount) - min(superstore_2011_2015$Discount),2)
medianDiscount <- median(superstore_2011_2015$Discount)
discountStats <- rbind(meanDiscount, stdDiscount, rangeDiscount, medianDiscount)
# Descriptive statistics of Sales
meanSales <- mean(superstore_2011_2015$Sales)
stdSales <- round(sd(superstore_2011_2015$Sales),2)
rangeSales <- max(superstore_2011_2015$Sales) - min(superstore_2011_2015$Sales)
medianSales <- median(superstore_2011_2015$Sales)
salesStats <- rbind(meanSales, stdSales, rangeSales, medianSales)
# Descriptive statistics of Profits
meanProfit <- mean(superstore_2011_2015$Profit)
stdProfit <- round(sd(superstore_2011_2015$Profit),2)
rangeProfit <- max(superstore_2011_2015$Profit) - min(superstore_2011_2015$Profit)
medianProfit <- median(superstore_2011_2015$Profit)
ProfitStats <- rbind(meanProfit, stdProfit, rangeProfit, medianProfit)
# Descriptive statistics of Shipping cost of the product
meanShippingCost <- mean(superstore_2011_2015$Shipping.Cost)
stdShippingCost <- round(sd(superstore_2011_2015$Shipping.Cost),2)
rangeShippingCost <- max(superstore_2011_2015$Shipping.Cost) - min(superstore_2011_2015$Shipping.Cost)
medianShippingCost <- median(superstore_2011_2015$Shipping.Cost)
ShippingCostStats <- rbind(meanShippingCost, stdShippingCost, rangeShippingCost, medianShippingCost)
combinedData <- cbind(discountStats, salesStats, ProfitStats, ShippingCostStats)
tableData <- combinedData
rownames(tableData) <- c('Mean', 'Standard Deviation', 'Range', 'Median')
colnames(tableData) <- c('Discount', 'Sales', 'Profit', 'Shipping Cost')
kable(tableData, caption = "<center><strong>Table 1: Statistics of 4 numerical variables</strong></center>", escape = FALSE,
format = "html") %>% kable_material(c("striped", "hover"))| Discount | Sales | Profit | Shipping Cost | |
|---|---|---|---|---|
| Mean | 0.1600 | 229.858 | 28.6569 | 23.83168 |
| Standard Deviation | 0.2065 | 623.250 | 234.2600 | 58.96000 |
| Range | 0.8000 | 22638.036 | 14999.9540 | 933.56000 |
| Median | 0.2000 | 54.490 | 8.6665 | 5.10000 |
Exploratory Data analysis
par(mar=c(5,8,4,2))
# Plot: Orders by each categories
colorname=RColorBrewer::brewer.pal(5,"Dark2")
y= barplot(table(superstore_2011_2015$Category),
ylim=c(0,8000),
col = colorname,
border="black",
main = "Bar Plot for Category Count",
xlab = "Category",
ylab = "Freqency of Category Count",
col.main="burlywood4",
col.lab="burlywood4") 
par(mar=c(5,8,4,2))
#Plot: Sales for different
ggplot() + geom_jitter(data = superstore_2011_2015,
aes(x = Region, y = Sales, fill = Region, colour=Region),
stat = "identity") +
labs(x = "Region", y = "Sales ($)", title = "Sales Distribution in different regions", subtitle = "Dataset: Superstore Data") +
theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust=1)) +
theme(plot.title = element_text(size=12, hjust=0.5, colour="black", vjust=-1)) +
theme(plot.subtitle = element_text(size=9, hjust=0.5, colour="black", vjust=-1))
par(mar=c(5,8,4,2))
#Plot: Sales Vs. Profit with mean and Linear Regression
plot(superstore_2011_2015$Sales, y=superstore_2011_2015$Profit,
pch = 19, col = "orange", fit="lm",
xlab = "Sales ($)",
ylab = "Profit ($)",
main = "Sales vs Distribution")
abline(h = mean(superstore_2011_2015$Profit), col = 'steelblue', lwd = 3, lty = 2)
reg_model <- lm(Profit ~ Sales, data = superstore_2011_2015)
abline(reg_model, col="purple") 
par(mar=c(5,8,4,2))
# Plot: Profit made by catergories
superstore_2011_2015 %>% ggplot(aes(x = Category, y = Profit)) +
geom_point(aes(width = 0.9, outlier.shape = NA,color = Category)) +
labs(title = "Profit distribution in Product categories",
subtitle = "Dataset: Superstore Data",
color = "Category") +
theme(plot.title = element_text(size=12, hjust=0.5, colour="black", vjust=-1)) +
theme(plot.subtitle = element_text(size=9, hjust=0.5, colour="black", vjust=-1))## Warning: Ignoring unknown aesthetics: width, outlier.shape
par(mar=c(5,8,4,2))
# Plot: Shipmode and Shipping cost
ggplot(superstore_2011_2015,
aes(x = Ship.Mode,
y = Shipping.Cost,
color = Ship.Mode)) +
geom_jitter(position=position_jitter(0.2), shape=17) +
theme_minimal() +
labs(x="Shipmode", y="Shipping Cost($)",
title = "Shipping cost for different shipping modes",
subtitle = "Dataset: Superstore Data",
color = "Shipping Mode") +
theme(plot.title = element_text(size=12, hjust=0.5, colour="black", vjust=-1)) +
theme(plot.subtitle = element_text(size=9, hjust=0.5, colour="black", vjust=-1)) +
scale_colour_manual(values=c("#AA2A64", "#BF403B", "#274530", "#779645")) +
scale_shape_manual(values=c("#EDB361", "#BF403B", "#274530", "#779645")) 
# Plot: Order count in each product category
par(mar=c(5,8,4,2))
categoryCount <- table(superstore_2011_2015$Category)
categoryCountPlot <- barplot(categoryCount,
main = "Order count in each product category",
ylab = "Count",
xlab = "Category",
width = 0.7, space = 0.15, ylim = c(0,7000),
cex.axis = 0.7, las = 1,
col = c("#B72E56", "#61B94C", "#7006C2"), border = NA)
text(categoryCountPlot, categoryCount,
labels = categoryCount, col = "white", pos = 1, cex= 0.8)
# Plot: Profit distribution
par(mar=c(5,8,4,2))
lossOutlier = which(superstore_2011_2015$Profit < 1.7280 | superstore_2011_2015$Profit > 70.7220)
lossOutlierData <- superstore_2011_2015[-lossOutlier,]
hist(lossOutlierData$Profit,
breaks = 25,
ylim = c(0,1000),
main="Histogram of Profit earned",
xlab = "Profit ($)",
ylab = "Count",
col = terrain.colors(10))
par(mar=c(5,8,4,2))
# Plot: Scatter plot of Total Sales vs Profit vs Discount
plot_ly(x=superstore_2011_2015$Total_Sales,
y=superstore_2011_2015$Profit,
z=superstore_2011_2015$Discount,
type="scatter3d", mode="markers", color=superstore_2011_2015$Sales) %>%
layout(scene = list(xaxis = list(title = "Sales"),
yaxis = list(title = "Profit"),
zaxis = list(title = "Discount Percentage")))# Plot 10: Time series analysis of Profit
# Typecasting to date
superstore_2011_2015$OrderDateColumn <- as.Date(superstore_2011_2015$`Order.Date`, "%m/%d/%Y")
superstore_2011_2015$OrderDateColumn <- format(as.Date(superstore_2011_2015$OrderDateColumn), "%Y-%m")
# Group by date and calculate Profit and Loss
timeSeriesProfitData <- aggregate(`Sales` ~ OrderDateColumn + Category,
data = superstore_2011_2015, FUN = sum, na.rm = TRUE)
ggplot(timeSeriesProfitData, aes(x = factor(OrderDateColumn), y = Sales, group = Category, color = Category)) +
geom_line(size = 1) +
scale_color_manual(values=c("#FDC534", "#007FFE", "#D61E29")) +
theme_gray() +
labs(x="Date", y="Profit($)",
title = "Profit obtained for different product categories",
subtitle = "Dataset: Superstore Data") +
theme(axis.text.x = element_text(angle = 45, hjust=1, size = 6)) +
theme(axis.text.y = element_text(hjust=1, size = 14)) +
theme(plot.title = element_text(size=12, hjust=0.5, colour="black", vjust=-1)) +
theme(plot.subtitle = element_text(size=9, hjust=0.5, colour="black", vjust=-1))
Hypothesis Testing
1. Hypothesis:
Ho : Average profit of the company in the US region is not $25
Ha : Average profit of the company in the US region is $25
#Ho : Average profit of the company in the US region is not $25
#Ha : Average profit of the company in the US region is $25
# t-test (One sample)
oneSampleData <- superstore_2011_2015[sample(nrow(superstore_2011_2015), 29), ]
t.test(oneSampleData$Profit, conf.level = .95, mu = 25) ##
## One Sample t-test
##
## data: oneSampleData$Profit
## t = -2.4863, df = 28, p-value = 0.01914
## alternative hypothesis: true mean is not equal to 25
## 95 percent confidence interval:
## -9.408078 21.677195
## sample estimates:
## mean of x
## 6.1345592. Hypothesis:
Ho : True difference in average profit of Office Supplies and Technology is not 0
Ha : True difference in average profit of Office Supplies and Technology is 0
OfficeSuppliesProfit <- subset(superstore_2011_2015, Category =="Office Supplies")
TechnologyProfit <- subset(superstore_2011_2015, Category =="Technology")
OfficeSuppliesRandomSample <- OfficeSuppliesProfit[sample(nrow(OfficeSuppliesProfit), 25), ]
TechnologyRandomSample <- TechnologyProfit[sample(nrow(TechnologyProfit), 25), ]
t.test(OfficeSuppliesRandomSample$Profit, TechnologyRandomSample$Profit)##
## Welch Two Sample t-test
##
## data: OfficeSuppliesRandomSample$Profit and TechnologyRandomSample$Profit
## t = -2.1034, df = 25.803, p-value = 0.04534
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -395.223587 -4.473461
## sample estimates:
## mean of x mean of y
## -15.0338 184.81473. Hypothesis:
Ho : True difference in average sales of West and East region is not 0
Ha : True difference in average sales of West and East region is 0
# t-test (Two sample)
westRegionSales <- subset(superstore_2011_2015, Region =="West")
eastRegionSales <- subset(superstore_2011_2015, Region =="East")
westRandomSample <- westRegionSales[sample(nrow(westRegionSales), 20), ]
eastRandomSample <- eastRegionSales[sample(nrow(eastRegionSales), 20), ]
t.test(westRandomSample$Sales, eastRandomSample$Sales, conf.level = 0.95) ##
## Welch Two Sample t-test
##
## data: westRandomSample$Sales and eastRandomSample$Sales
## t = -0.31458, df = 37.605, p-value = 0.7548
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -304.9933 222.9776
## sample estimates:
## mean of x mean of y
## 210.8363 251.8442Data distribution of Shipping cost for Corporate vs Consumer segments
consumerShippingCost <- subset(superstore_2011_2015, Segment =="Consumer")
corporateShippingCost <- subset(superstore_2011_2015, Segment =="Corporate")
plotData <- subset(superstore_2011_2015, Segment =="Corporate" | Segment =="Consumer")
ggplot(plotData, aes(x = plotData$Segment, y = plotData$Shipping.Cost,
color=plotData$Segment)) +
geom_jitter(position=position_jitter(0.2)) +
theme_light() +
labs(y="Shipping costs ($)", x="Segments", title = "Shipping cost for Corporate vs Consumer segments",
subtitle = "Dataset: Superstore data") +
theme(plot.title = element_text(size=14, hjust=0.5, colour="black", vjust=-1)) +
theme(plot.subtitle = element_text(size=10, hjust=0.5, colour="black", vjust=-1)) +
scale_colour_manual(values = c("#4AB097", "#BB203C", "#FB761F")) +
scale_shape_manual(values=c(1,17,19))
4. Hypothesis:
Ho : True difference in average shipping cost of Consumer and Corporate segments is not 0
Ha : True difference in average shipping cost of Consumer and Corporate segments is 0
# t-test (Two sample)
consumerRandomSample <- consumerShippingCost[sample(nrow(consumerShippingCost), 24), ]
corporateRandomSample <- corporateShippingCost[sample(nrow(corporateShippingCost), 24), ]
t.test(consumerRandomSample$Shipping.Cost, corporateRandomSample$Shipping.Cost, conf.level = 0.95) ##
## Welch Two Sample t-test
##
## data: consumerRandomSample$Shipping.Cost and corporateRandomSample$Shipping.Cost
## t = 1.9364, df = 24.72, p-value = 0.06434
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -2.946117 94.686117
## sample estimates:
## mean of x mean of y
## 59.25375 13.383755. Hypothesis:
Ho : Company’s average sales is higher in the West region than East region of the US
Ha : Company’s average sales is higher in the East region than West region of the US
# t-test (Two sample)
t.test(westRandomSample$Sales, eastRandomSample$Sales, conf.level = 0.95,
alternative = "greater") ##
## Welch Two Sample t-test
##
## data: westRandomSample$Sales and eastRandomSample$Sales
## t = -0.31458, df = 37.605, p-value = 0.6226
## alternative hypothesis: true difference in means is greater than 0
## 95 percent confidence interval:
## -260.8419 Inf
## sample estimates:
## mean of x mean of y
## 210.8363 251.8442Correlation and Regression analysis
# Correlation between Sale, Discount, Profit, Quantity and Shipping cost
corrData <- data.frame(Sales = superstore_2011_2015$Sales,
Discount = superstore_2011_2015$Discount,
Profit = superstore_2011_2015$Profit,
Quantity = superstore_2011_2015$Quantity,
`Shipping Cost` = superstore_2011_2015$Shipping.Cost)
ggcorrplot(cor(corrData),
hc.order = TRUE,
type = "lower", lab = TRUE,
insig = "blank",
ggtheme = ggplot2::theme_grey(),
title = "Correlation between Company's Sales stats")
# Linear Regression Model
model2 <- lm(Shipping.Cost ~ Sales + Category, data = superstore_2011_2015)
summary(model2)##
## Call:
## lm(formula = Shipping.Cost ~ Sales + Category, data = superstore_2011_2015)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1398.26 -10.55 -4.82 -2.02 773.25
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 16.053203 0.966937 16.602 <2e-16 ***
## Sales 0.062090 0.000709 87.579 <2e-16 ***
## CategoryOffice Supplies -11.032639 1.098905 -10.040 <2e-16 ***
## CategoryTechnology 0.858914 1.371787 0.626 0.531
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 43.04 on 9990 degrees of freedom
## Multiple R-squared: 0.4673, Adjusted R-squared: 0.4671
## F-statistic: 2921 on 3 and 9990 DF, p-value: < 2.2e-16# PLot1
p1 <- ggplot(superstore_2011_2015, aes(x = Sales,
y = Shipping.Cost,
col = Profit)) +
xlim(c(0,7500)) + ylim(c(0,1000)) +
geom_point() +
theme_minimal() +
theme(axis.text=element_text(size=12)) +
geom_smooth(method="lm", formula = y~x, color = "red") +
facet_grid(~Segment)
p1 + scale_color_gradient(low="pink", high="blue")## Warning: Removed 13 rows containing non-finite values (stat_smooth).## Warning: Removed 13 rows containing missing values (geom_point).